Communication pubs.acs.org/crystal
The Multiple Structures of Vaterite Raffaella Demichelis,*,† Paolo Raiteri,† Julian D. Gale,† and Roberto Dovesi‡ †
Nanochemistry Research Institute, Department of Chemistry, Curtin University, PO Box U1987, Perth, WA 6845, Australia Dipartimento di Chimica, Università degli Studi di Torino and NIS -Nanostructured Interfaces and Surfaces - Centre of Excellence, Via Giuria 7, 10125 Torino, Italy
‡
S Supporting Information *
ABSTRACT: For many years the nature of the disordered structure of vaterite, a calcium carbonate polymorph that plays a significant role in biomineralisation, has been debated. In the past year, two independent studies (Angew. Chem., Int. Ed., 51, 7041; CrystEngComm, 14, 44) have proposed new, yet different models on the basis of electron diffraction experiments and ab initio calculations, respectively. Here, it is shown that there are at least three effectively isoenergetic models that are equally likely to describe the vaterite structure at room temperature. These distinct models, each consisting of multiple structures, can explain the disorder of vaterite in terms of different orientations of the carbonate anions, multiple stacking sequences of the carbonate layers, and possible chiral forms. Hence, vaterite is not a single “disordered” structure but should instead be considered as a combination of different forms, each of which can exhibit rapid interchange between multiple structures that exhibit similar average properties.
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similarities, the structures arrived at are not the same. This raises the question of whether it is possible to reconcile the differences between these models and to arrive at a unified interpretation of the structure of vaterite? Before addressing the above question, it is necessary to highlight the key results from both of the aforementioned studies. In the work of Demichelis et al.,6 all of the proposed ordered structures available in the literature at that time were re-examined using ab initio quantum mechanical calculations. On the basis of this, all of the existing models turned out to be thermodynamically unstable, corresponding either to transition states or to high-energy structures. A new model was proposed that considers vaterite as a dynamic system, where small rotations of the CO32− units are allowed at ambient temperature. The true structure of vaterite is then described as a combination of at least three different minimum energy configurations (with space groups of P1121, P65, and P3221). These minima are then able to interconvert through CO32− rotations, leading to a Boltzmann-weighted average structure
aterite (CaCO3) is a metastable calcium carbonate polymorph crystallized by several living organisms as part of their hard tissues, through the interaction of CaCO3 clusters and amorphous nanoparticles (ACC) with biomolecules.1 The nucleation of calcium carbonate itself is attracting considerable attention since recent observations suggest that it occurs via a mechanism that differs from the expectations of classical nucleation theory.2 Recently, it has been shown that vaterite can also naturally crystallize in abiotic environments at elevated CO2 pressures, through experiments aimed at demonstrating how calcium carbonates can crystallize in astrophysical environments.3 Therefore an accurate description of the atomic details of CaCO3 structures is required to fully understand their nucleation, polymorph selection, and crystal growth under both biogenic and abiotic conditions.4 The structure of vaterite has puzzled scientists for over half a century, and many authors have proposed very different interpretations of the available experimental data (summarized in refs 5 and 6). However, in the last year, major advances have been made independently through state-of-the-art ab initio calculations (in the work of Demichelis et al.6) and through advanced experimental techniques by Mugnaioli et al.5 While both studies propose new models for vaterite that share © XXXX American Chemical Society
Received: February 22, 2013 Revised: April 20, 2013
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close to the space group of P6522 originally proposed by Wang and Becker.7 In the subsequent paper by Mugnaioli et al.,5 two models with C2/c (“2-layer”) and C1̅ (“6-layer”) symmetry have been proposed, as a result of automated electron diffraction experiments. These structures are found to have a density of 2.76 g cm−3, which is higher than that directly measured (2.54 g cm−3) and that calculated on the basis of the previously proposed experimental structures (2.65 g cm−3) by 8.6% and 5.1%, respectively.8 Aside from the density, the main difference with respect to the structures proposed by Demichelis et al.6 lies in the sequence of the carbonate layers along the quasihexagonal c axis. Quantum mechanical ab initio calculations based on Density Functional Theory (using the PBEsol9 functional) have been applied to investigate the two structures proposed by Mugnaioli et al.,5 to understand whether there is a connection with the alternative model proposed by Demichelis et al.6 The same methodology,10 computational parameters, and basis set as in ref 6. have been used and are briefly described in the Supporting Information. The 2-layer structure (C2/c) of Mugnaioli et al.5 relaxes to a density of 2.67 g cm−3, which is in line with experimental estimates. However, this configuration turns out to be +1.5 kJ/ mol per formula unit (fu) higher in energy than the most stable structure of Demichelis et al.6 (P3221). By computing its phonon spectrum, two imaginary vibrational frequencies are obtained, indicating that this structure is actually a transition state rather than a stable minimum energy structure. By displacing the structure along the eigenvectors for the unstable modes, two minimum energy structures are arrived at with the space groups of C2 and Cc. These new structures now have energies relative to the P3221 model of +0.2 (C2) and +1.0 (Cc) kJ/mol. The main transformations observed during the structural relaxations consist of rotations and minor rearrangements of CO32− units (see movie in the Supporting Information). The above analysis demonstrates that the 2-layer structure of Mugnaioli et al.5 belongs to a separate energy basin with respect to the structures proposed by Demichelis et al.6 Here, each broad basin comprises several distinct minima of different symmetry that have barriers to interconversion that can readily be crossed at ambient conditions. Despite this separation, a comparison between the replicated 2-layer monoclinic and the hexagonal structures (Figure 1) reveals striking similarities. In particular, we note that one structure could be converted into the other by exchanging two molecular (001) planes (adopting the Miller indices for the pseudohexagonal cell). This opens up the fascinating possibility that in vaterite, there exists a stacking disorder of the CO32− planes, first observed by Qiao and Feng using HRTEM and SAED measurements on natural samples of vaterite,11 on top of the rotational freedom of CO32− units already predicted by Demichelis et al.6 This provides a basis for the interpretation of the experimental disorder observed in vaterite and can reconcile all the crystalline structures proposed in the past within a unified framework. In order to discover whether there are other possible stacking combinations, starting from the P3221 structure and removing all symmetry constraints, we have explored all the possible permutations of the 6 planes along the c axis (labeled A, B, C, A′, B′, and C′, as given in Figure 1). This results in 50 structures that are inequivalent by translation. From all the existing models of vaterite, we observe that only sequences that
Figure 1. 2-Layer monoclinic (left) and hexagonal (right) structures, viewed along the a lattice parameter. The monoclinic primitive cell is shown in black (dashed for supercell), its pseudohexagonal supercell and the hexagonal unit cell in blue. The stacking sequence of CO32− layers refers to the orientation of the CO32− units with a C−O bond parallel to a: planes with the same shift (0,1/3, 2/3) with respect to b are labeled with the same letter (A, B, or C), while planes with C−O pointing toward +a/−a are labeled with and without a prime, respectively. O, Ca, and C atoms are shown in red, green, and gray, respectively.
alternate “prime” with “nonprime” planes are allowed; only 5 out of the 50 permutations fulfill this constraint. Of these, 3 belong to the hexagonal group and 2 to the 2-layer monoclinic group. Geometry optimization of the latter two leads to structures in the space group of C2. Geometry optimization of the first three results in structures either in the space group of P3221 or in its mirror image, P3121. To the best of the authors’ knowledge, optical experiments aimed at investigating the existence of vaterite enantiomers have never been performed. However, 2 out of 3 hexagonal minimum energy structures are in chiral space groups12 (P65|P61, P3221|P3121, as well as the transition states P6522|P6122), and based on pure calculations on the infinite crystal, each of the two enantiomers is equally likely to occur. With consideration that vaterite can be preferentially nucleated under biogenic conditions, it may be that the chirality of this family of structures could be significant and lead to preferential formation of one enantiomer in the presence of biomolecules. The second monoclinic model proposed by Mugnaioli et al.5 (C1̅) corresponds to a sequence of 6 layers in which B and C′ are missing (Figure 2). The relaxed structure is 0.6 kJ/mol per
Figure 2. Primitive cell of the 6-layer monoclinic structure (C1)̅ by Mugnaioli et al.5 viewed along a. Colors and symbols are the same as in Figure 1. B
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different structures may coexist at ambient temperature. They also suggest that extended defects related to different sequences of layers, such as stacking faults, are very likely to occur in experimental samples. However, on the basis of these static calculations, we cannot predict whether these defects are the result of kinetics or external influences during the crystal growth or are the result of thermal equilibrium within the crystal. The above computed data include only the electronic and vibrational contributions. However, for disordered systems, the configurational entropy may also be significant. An estimation of this quantity can be made by considering the independent permutations of the hexagonal structure, leading to 3 and 2 energetically equivalent hexagonal and 2-layer monoclinic structures, respectively. For the C1 structures there must be at least 3 combinations of planes having the same energy (the one in Figure 2, B′BC′AB′B, and C′CA′BC′C). If we include the configurational entropy, estimated through the Boltzmann formula Sconf = k B ln W, where W is the number of configurations, the average ΔS and ΔG of Table 1 become +0.9 J/(mol K) and +3.4 kJ/mol, respectively. This leads to improved agreement for the entropy with experiment, though the influence on the overall free energy is not significant. From the above, it is now clear that a number of structures differing in their layer stacking might exist, and that the structures proposed by Mugnaioli et al.5 and by Demichelis et al.6 are just three in this possible range of configurations. The complete energy landscape associated with the structures considered is shown in Figure 3. Lattice parameters and fractional coordinates of the monoclinic structures are reported in the Supporting Information; the hexagonal structures are reported in the Supporting Information of ref 6. A qualitative prediction of the presence of basins corresponding to different layer stackings was made by Wang and Becker,13 as a result of molecular dynamics simulations.
formula unit higher in energy than the most stable hexagonal structure (P3221) and has a density closer to the experimental value (2.68 g cm−3). However, this structure also corresponds to a transition state. Again, transformation of the structure by removing the imaginary vibrational modes (only rotations and minor displacements of the CO32− units are observed) leads to two distinct minimum energy structures both in the space group of C1 (+0.4 and +0.5 kJ/mol). Analysis of the thermodynamic stability relative to calcite, the most stable form of CaCO3 at ambient conditions, is given in Table 1. Here, data are given for the structures in the Table 1. Thermodynamic Quantities for the Transformation of Vaterite to Calcite at 298 K, Plus the Relative Probability of Each Vaterite Structure Based on a Boltzmann Distribution P3221 (P3121) P65 (P61) P1121 Cc C2 C1 C1 average exp18
ΔE
ΔHa
ΔSa
ΔGa
p
3.1 3.8 3.6 4.0 3.2 3.5 3.6
3.3 3.8 3.9 4.0 3.2 3.7 3.9 3.6 3.60
+0.8 −1.1 +1.2 −0.5 −1.0 +1.7 +2.0 +0.4 +1.30
3.1 4.1 3.6 4.2 3.5 3.2 3.3 3.5 3.21
0.132b 0.088b 0.110 0.086 0.113 0.127 0.123
a
Electronic energy (E), enthalpy (H) and free energy (G) in kJ/mol; entropy (S) in J /(mol K). The relative population of the configurations, p, is calculated on the basis of their ΔG. bThe population of the mirror image is also considered.
hexagonal, 2-layer, and 6-layer monoclinic basins and compared against the experiment. The energetic window is very narrow, and the relative populations suggest that all these apparently
Figure 3. Energy landscape of the hexagonal, 2-layer, and 6-layer basins. Vertical lines separate the three different basins: within the same window, structural interconversion happens at 298 K by rotation of the CO32− units. C
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However, because no calculation of the vibrational frequencies was performed at the ab initio level, together with the poor quality of their force field (as recognized by the authors themselves), led Wang and Becker to propose C2/c and P6522 as the most stable and a slightly less stable structures, respectively, whereas they both actually correspond to transition states. The results of this study are significant because (i) they confirm the previous interpretation of vaterite as a dynamic structure (rotational freedom of CO32− units at room temperature),6 (ii) they validate the hypothesis of different possibilities for the layer stacking in vaterite as a second source of disorder, resulting in the presence of at least three basins of hexagonal, 6-layer, and 2-layer monoclinic structures,5,6,11 (iii) they show that different stacking arrangements are all energetically close on the scale of thermal energy, though nothing can be said at this stage about possible mechanisms of interconversion between the hexagonal and the monoclinic groups of structures, and (iv) they add a possible third element of complexity in the description of the structure, namely chirality. From a broader perspective, it is not unreasonable to hypothesize that a wide variety of structures exhibiting minor structural and energetic differences might exist in nature. Wehrmeister et al.14 arrived at similar conclusions on the basis of Raman spectroscopy measurements on a wide variety of natural and synthetic samples. For example, the environmental conditions might favor the formation of one particular layer stacking or chirality, without fully excluding the formation of the other possibilities. Also, nucleation of vaterite in contact with a chiral organic molecule may promote the formation of one of the noncentrosymmetric structures identified. The formation mechanism of vaterite itself, which involves the formation of differently oriented crystalline domains both from supersaturated solutions15 and from ACC nanoparticles,16 does not exclude the option of the various crystallites to grow with a slightly different structure in the same solution. Experimental support for the present hypothesis that vaterite can exist as multiple structures actually appeared after the revised version of this manuscript had been submitted.17 Through the application of transmission electron microscopy, Kabalah-Amitai et al. have shown that there are “at least” two different structures that coexist in vaterite crystals: one that exhibits hexagonal symmetry (that in our model would be the hexagonal basin) and the other one that remains undetermined (which, according to our predictions, could be one of the monoclinic basins). On the one hand, the existence of several form of vaterite would explain its natural disorder, while on the other hand, it suggests that perhaps not all samples of vaterite might be the same, while still exhibiting similar spectroscopic properties. On the basis of the above findings, it would be appropriate to regard vaterite as a group of related structures that differ in the order of stacking within the carbonate layers, rather than as a single disordered material.
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Communication
AUTHOR INFORMATION
Corresponding Author
*E-mail: raff
[email protected]. Author Contributions
R. Demichelis, P.R., and J.D.G. performed and analyzed the simulations. R. Dovesi provided the code. All the authors contributed to the writing and editing of the manuscript. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors thank the Australian Research Council for funding through the Discovery grant DP0986999 and Curtin University for funding through the Curtin Research Fellowship scheme. iVEC@murdoch and NCI supercomputing facilities are also acknowledged for the provision of computer time.
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REFERENCES
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ASSOCIATED CONTENT
* Supporting Information S
Computational details; lattice parameters and fractional coordinates of the optimized monoclinic structures; cif files of the minimum energy structures; example movie of structural interchange through carbonate rotation. This material is available free of charge via the Internet at http://pubs.acs.org. D
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(18) Königsberger, E.; Königsberger, L. C.; Gamsjäger, H. Geochim. Cosmochim. Acta 1999, 63, 3105−3119.
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